Here we did not discuss at length the role played by integrability. Some aspects of it can be found in [1]}. On the other hand, it should be clear that the methods presented here extend to other contexts such as defect CFTs. Some investigations in this direction appeared already in [2]}, but more work is in progress which seems to provide a non-trivial and highly structured modification of the theory described in the text. Finally, the spaces of \(K\) -spherical functions have been studied recently in [3]}, where the authors placed a particular emphasis on their representation through the Eisenstein integral. Investigation of analytic properties of these functions also seem to be a necessary requirement for analysis of crossing equations. We hope to turn to this question in the future.
